Simplify the expression without a calculator. \( \log \left(10^{\sqrt{7}}\right)=\square \)

To simplify the expression \( \log \left(10^{\sqrt{7}}\right) \), you can use the logarithmic property that states \( \log_b (a^c) = c \cdot \log_b (a) \). In this case, we have \( \log \left(10^{\sqrt{7}}\right) = \sqrt{7} \cdot \log (10) \). Since \( \log (10) = 1 \), the expression simplifies to \( \sqrt{7} \cdot 1 = \sqrt{7} \). Therefore, \( \log \left(10^{\sqrt{7}}\right) = \sqrt{7} \). So, the answer is: \(\sqrt{7}\)